Problem
An artist who sales his paintings to a gallery is paid an γ share of the revenue which gallery earns from selling his painting to consumers, where the revenue is R = pq. p = $20 is the competitive market price for paintings, and q is the number of paintings sold. Let us assume that the gallery only sales this artists paintings and the gallery's cost is C(q) = 2q 2 . Determine the equilibrium, and compare it to the outcome that maximizes the sum of the payment to the painter plus the gallery's profit. Show your answer using math and a graph.